Electronic Stability Control for Improving Stability for...

Research ArticleElectronic Stability Control for Improving Stability for anEight In-Wheel Motor-Independent Drive Electric Vehicle

Yu Zhao 12 and Chengning Zhang12

1National Engineering Laboratory for Electric Vehicle Beijing Institute of Technology Beijing 100081 China2Collaborative Innovation Center for Electric Vehicle in Beijing Beijing Institute of Technology Beijing 100081 China

Correspondence should be addressed to Yu Zhao sszhaoyubiteducn

Received 16 December 2018 Revised 21 March 2019 Accepted 26 March 2019 Published 17 April 2019

Academic Editor Davood Younesian

Copyright copy 2019 YuZhao andChengning Zhang(is is an open access article distributed under the Creative CommonsAttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An electronic stability control (ESC) based on torque distribution is proposed for an eight in-wheel motor-independent driveelectric vehicle (8WIDEV) (e proposed ESC is extremely suitable for the independent driving vehicle to enhance its handlingstability performance (e vehicle model is established based on a prototype 8WIDEV A hierarchical control strategy whichincludes a reference state generation controller an upper-level vehicle controller and a lower-level optimal control allocationcontroller is utilized in the ESC (e reference state generation controller is used to obtain the ideal reference vehicle state (eupper-level vehicle controller is structured based on sliding mode control which obtains the generalized objective force during8WIDEV movement therein considering the side slip angle and yaw rate (e lower-level optimal control allocation controllerattempts to allocate the vehiclersquos objective force in each motor optimally and reasonably (e model is validated by fieldmeasurement results under the step input condition and snake input condition Simulation results from a hardware-in-the-loop(HIL) simulation platform indicate that the ESC based on the optimized allocation proposed for 8WIDEV achieves better stabilityperformance compared with direct yaw moment control (DYC)

1 Introduction

(e structure of an electric vehicle driven by in-wheelmotors is different from that of traditional vehicles drivenby internal combustion engines in that it does not use anengine or transmission places the motor inside the hubappropriately and uses a battery as the power supply (eeight in-wheel motor-independent drive electric vehicle(8WIDEV) has eight independent controllable motorswhich has the potential to improve the vehicle handlingstability [1 2] (e 8WIDEV system is a typical redundantlyactuated system and has greater flexibility than four in-wheelmotor-independent drive electric vehicles [3] Due to itsmany advantages 8WIDEV is widely used as a special ve-hicle However 8WIDEV has different characteristics from4WIDEV a high center of mass and complicated drivingconditions Because the executor has numerous and morecomplex nonlinear characteristics the vehicle controlstrategy is more complicated [4]

Currently there are three commonly used controlstructures for the dynamic control of a vehicle driven by in-wheel motors decentralized centralized and hierarchicalcontrol structures Because of its flexibility the hierarchicalcontrol strategy is more suitable for solving complex non-linear and redundant systems with executive constraintscompared with decentralized and centralized controlstructures [5ndash8] (e hierarchical control structure uses acontrol law in the upper controller to solve the complex andnonlinear problem of the vehicle (e lower-level optimalcontrol allocation controller used in the hierarchical controlstructure assigns the target moment to the actuators underthe constraint condition [9 10] A commonly used controlmethod considers the problem as a control allocationproblem with constraints [11 12] Most research on vehiclecontrol systems is now directed at 4WIDEV having madegreat progress [13ndash15] A state feedback-based controlsystem using direct yaw moment control is set up for4WIDEV effectively reducing the modeling difficulty

HindawiShock and VibrationVolume 2019 Article ID 8585670 21 pageshttpsdoiorg10115520198585670

Comparing with the widely used model following controlthe stability of the vehicle is improved [3 8 16] A controlstrategy with an optimal target is proposed to improve theelectric drive vehicle dynamic stability and maneuver-ability In lower-level optimal control allocation control-lers an optimization algorithm is used to distribute themotor torque to achieve effective control [17 18] Based ona hierarchical control structure an ESC system suitable fora 4WIDEV is presented (ree levels of control logic aredesigned in the ESC system which contains a torquedistribution algorithm based on a minimum-objective-function to enhance the vehiclersquos stability [19] Fully uti-lizing the hierarchical structure a linear quadratic regu-lator control method is obtained by controlling the yaw rateto design the upper-level controller and a fast calculationmethod is used to achieve a fast motor torque distribution[20] Taking two variables reflecting the advantages anddisadvantages of the vehiclersquos lateral movement in themotion control unit the objective yaw moment is obtainedby fuzzy logic control However this method is highlydependent on engineering and a lack of control accuracy[21] A new control method is proposed based on modelpredictive control (MPC) theory to address the issues ofmultiple objectives with constraints which can maximizethe regeneration efficiency while maintaining the vehicledynamics [22] (ese methods focus on the vehicle torqueallocation but do not optimize the vehicle handling stabilityfor vehicle motion control

However fewer studies have focused on the 8WIDEVwith high weights As the number of driving wheels in-creases the 8WIDEV becomes applicable to more com-plicated driving conditions given its greater flexibility andmaneuverability To improve the 8WIDEV handling sta-bility the longitudinal dynamic control and lateral dy-namic control are constructed (e target lateral force andtarget yaw moment are obtained by controlling the twocorresponding vehicle variables in lateral control [23] Ahierarchical control allocation strategy is developed byconsidering the real-time performance of the control formultiaxle land vehicles equipped with independent drivingwheels [24] Because the vehiclersquos steering wheel angle isnot large the distribution of the motor torque needs tosatisfy the demanded lateral force of the vehicle and thetorque of the motor readily experiences a saturated am-plitude Vehicle stability control is mainly reflected in twovariables Vehicle handling stability is not only related tothe vehicle longitudinal speed but also directly related tovehicle yaw speed and side slip angle which is directlyrelated to the vehicle heading angle and determines theperformance of the vehicle trajectory tracking In additionalthough the two variables are controlled simultaneouslysometimes and the target yaw moment and lateral force areobtained the motor output torque readily becomes satu-rated for a vehicle without active steering [10 23] Based onnonlinear control theory a fuzzy logic method the yawmoment is obtained by controlling the lateral slip angle andyaw rate However it is not easy to establish precisemathematical relations for this control method and it ismore dependent on experience [21]

(e yaw rate is mathematically related to yaw momentthus it can be directly controlled However the re-lationship between the side slip angle and yaw momentrepresents an ldquoun-matching systemrdquo which can beexpressed as that the side slip angle being tracked to anideal stare quantity by controlling the yaw rate as an in-termediate variable however the actual yaw rate is notsufficient to track its reference value [25] (e requiredlateral force can be calculated via steering angle controland the expected yaw moment is obtained by fully utilizingthe yaw rate (is integrated control method can be usedby active steering vehicles [26] (e control configurationvehicle principle is structured to improve the flexibilityand performance of the structure layout Although thismethod can focus on the side slip angle control it is onlysuitable for steer-by-wire vehicles which presents limi-tations for use in vehicles without active steering orauxiliary steering

Most control allocation rules now adopt traditionalallocation methods such as average allocation and directcontrol allocation (ese methods are faster in calculatingthe torque distribution however their torque allocationmethod is simple (e vehicle dynamics constraints andthe optimization of the torque distribution need to be fullyconsidered [27 28] Considering the nonlinear saturationand coupling relationship of the tire force and torquesaturation amplitude of the drive motor a lower-leveloptimal control allocation controller is constructed Anonlinear tire is regarded as a more extensive ldquoconstrainednonlinear actuatorrdquo in the control allocation (eoptimization-based control allocation method withweighted least square (WLS) is used for the torque forcedistribution this can effectively increase the computationspeed [29]

In this paper ESC based on a hierarchical controlstrategy is established to enhance the performance of thehandling stability and trajectory capability of 8WIDEV(e hierarchical control structure includes the referencestate generation controller the upper-level vehicle con-troller and the lower-level optimal control allocationcontroller By utilizing the classic reference model of thevehicle a monorail of four-axle vehicles based on a twoDoF model is established to obtain the required referencestate of the vehicle (e reference state generation con-troller is designed using the reference state of the vehicleIn contrast to the linear control method attempting toconsider vehicle nonlinearity and uncertainty the upper-level vehicle controller is built using the nonlinear controlmethod therein achieving strong robustness to vehicleparameter uncertainties and external disturbances (eupper-level vehicle controller includes a yaw momentsynthesis controller therein considering the two controlvariables related to lateral motion tracking while adjustingthe weight coefficient Actuator torque allocation for re-dundant systems is modeled as a constrained optimizationproblem (e main contribution of this paper lies in thefollowing points First based on prototype vehicle pa-rameters a dynamic model of an 8WIDEV is established(is model can fully reflect the dynamic characteristics of

2 Shock and Vibration

the vehicle and provide a favorable basis and conditionsfor verifying the control method (e effectiveness of thevehicle model is verified through comparison simulations inMATLABSimulink with the experimental results for theprototype vehicle Second the vehicle slip angle and the yawrate tracking are realized via sliding mode control and thecorresponding yaw moment is obtained (is provides theadvantage of avoiding the saturation of the motor torquecaused by satisfying the lateral force requirement(e stabilitycontrol strategy proposed in this paper improves the stabilityof vehicles according to the simulation and contrasts withDYC control (ird because most previous stability controlstudies on the 8WIDEV lack validation in this paper ahardware-in-the-loop (HIL) experiment verifies that the ESCproposed improves vehicle handling and stability [30 31]

(e structure of this paper is divided into the fol-lowing main parts first the 22-DoF vehicle dynamicmodel is introduced including the vehicle body modelsuspension model wheel model tire model and electricmotor model Second a vehicle control strategy for the8WIDEV based on a hierarchical structure is proposedwhereby the ESC system in the vehicle improves thevehicle handling stability Finally analysis of a simulationexperiment and a hardware-in-the-loop (HIL) experi-ment to verify the vehicle dynamic model established inMATLABSimulink demonstrates the dynamic charac-teristics of the 8 times 8 prototype vehicle and verifies theeffectiveness of the control strategy proposed in thispaper to improve the vehicle handling stability and goodtrajectory tracking ability Finally we conclude the papertherein describing valuable observations obtained in thisstudy

2 Vehicle Model

(e research in this paper focuses on a 8WIDEV handlingstability project (e 8times 8 prototype vehicle is shown inFigure 1(e 8WIDEV is equipped with eight independentlycontrollable in-wheel motors which can be described aslarger unsprungmasses(e importance of vehicle dynamicscontrol is to establish a nonlinear vehicle dynamics char-acteristic model that can reflect the vehicle dynamicscharacteristics

(is section mainly describes the 22-DoF vehicle dy-namic mode including a model of the vehicle body sus-pension tires wheels and electric motor (e vehicle bodymodel usually only considers motion in three directionsConsidering the static and unsteady problem of the sus-pension system and the body in the vertical dynamics asuspension model based on the static equilibrium is con-structed and the vehicle body model considers the 6-DoF ofthe body Considering the effects of the slip rate side slipangle road adhesion coefficient concerning the tire forcesnonlinear saturation and coupling of the total tire force atire model based on the nonlinear saturation and couplingcharacteristics of the tire is established Table 1 lists the mainparameters of the 8WIDEV(e parameters of the 8WIDEVare obtained from the manufacturer (e vehicle bodymodel suspension model wheel model tire model and

motor model constitute the 8WIDEV dynamic model Asdescribed in the previous paragraph the following sectionsmainly describe the modeling of each part of the 8WIDEVbased on a variety of theoretical methods (e 8WIDEVdynamic model is validated in Experiment and Simulation

21VehicleBodyModel Figure 2 shows the planermotion ofthe vehicle body which is considered as a general rigid bodywith 6-DoF including translational and rotational degrees offreedom in three directions (e equations of motion for thevehicle model can be expressed as follows

max 11139444

1Fxij1113872 1113873minusFf minusFw minusFi (1)

may 11139444

1Fyij1113872 1113873 (2)

mbaz 11139444

1Fzsij (3)

Iy _ωy plusmn11139444

1li Fzsi1 + Fzsi2( 1113857 + mbghc sin θ (4)

Ix _ωx di 1113944

4

1Fzsij minusFzsij1113872 1113873 + mbghc sin θ (5)

Figure 1 8times 8 prototype vehicle

Table 1 (e basic structure parameters of the 8WIDEV

Parameter Symbol Unit ValueVehicle weight m kg 21000Spring weight mb kg 17000Track width Db m 26Distance from axles tocentroid l1l2l3l4 m 223081119

261Vehicle moment inertia Iz kgmiddotm2 33625Centroid height hc m 11Tire radius Rw m 06Electric wheel mass Mw kg 400Wheel rotational inertia Iw kgmiddotm2 120Suspension stiffness Ks kNmiddotmminus1 200Suspension damping Cs kNmiddotsmiddotmminus1 400Fixed reducer ratio ig mdash 11

Shock and Vibration 3

Iz _ωz di Fxi1 minusFxi2( 1113857 plusmn 11139444

1li Fyi1 minusFyi21113872 1113873 (6)

where Ff mgfr cos αf and Fw 12CDAjρv2x Ff and Fw

are the rolling resistance and air resistance respectively Fi isthe slope resistance Fi mg sin αf ax ay and az are thelongitudinal lateral and vertical acceleration of the ve-hicle respectively vx vy and vz are the longitudinallateral and vertical velocity of the vehicle respectivelyωx ωy and ωz denote the roll pitch and yaw rate re-spectively ϕ and θ are the roll angle and pitch anglerespectively and Fxij Fyij and Fzsij represent the lon-gitudinal force lateral force and vertical force in thevehicle coordinate system respectively To clarify thevariables i 1234 denotes the firstsecondthirdfourth axis and j 12 denotes the leftright wheel ofthe vehicle hc di and li represent the centroid heighttrack width and distance from the axles to the centroidm and mb are the vehicle mass and spring mass re-spectively fr αf CD Aj and ρ denote the rolling re-sistance coefficient gradient air resistance coefficientwindward area and air density respectively and Ix Iyand Iz are the moment of inertia around the x-axis y-axisand z-axis respectively

(e tire coordinate system is shown in Figure 3 (erelationship between the tire force in the vehicle coordinatesystem and in the tire coordinate system can be expressed bythe following equations which provide representations indifferent coordinate systems

Fxij Fxwij cos δij minusFywij sin δij (7)

Fyij Fywij sin δij minusFywij cos δij (8)

22 SuspensionModel (e suspension and vehicle body inthe vehicle vertical dynamics represent a statically in-determinate problem Based on the traditional displace-ment method the suspension force and vertical force ofthe tire are solved In addition the suspension model isbuilt based on suspension parameters and suspensionsystem theory of 8WIDEV and mainly refers to the dy-namic method of multiaxle vehicle suspension modeling[23] First the suspension force F1zsij and tire load F2zsij

under the static balance of the vehicle are solved by thedisplacement method Second the dynamic suspensionforce F2zsij and the dynamic tire load F2zwij are calculatedin the motion state relative to the static equilibrium statebeing based on the motion differential equation

Under static balance of the vehicle the balance of thevehicle vertical force and the balance equation of the bodymoment are given as follows

F1zs1 + F1zs2 + F1zs3 + F1zs4 mbg

F1zs1l1 + F1zs2l2 F1zs3l3 + F1zs4l4(9)

41 31 21 11

42 32 22 12

ωZ O

Fxw41

Fyw41

α41

v41

Fxw42

Fyw42

α42v42

Fxw31

Fyw31

α31

v31

Fxw32

Fyw32

α32v32

Fxw21

δ21α21

v21

Fyw21

Fxw11

δ11α11

v11

Fyw11

Fxw22

δ22α22

v21

Fyw22

Fxw12

δ12α12

v12

Fyw12

y

x

l1l4

l2l3

bi = 2divx

vyβ

V

Figure 2 xoy planer motion of the 8WIDEV body

Fxwij

Fywij

xw

yw

vwσ

α

Figure 3 Tire coordinate system


It is assumed that the stiffness of each axle suspension isthe same and the static suspension force of each axle isobtained

F1zs1 lb minus lal1

4lb minus l2ambg

F1zs2 lb minus lal1 minus la minus 4l1( 1113857 l1 minus l2( 1113857

4lb minus l2ambg

F1zs3 lb minus lal1 minus la minus 4l1( 1113857 l1 + l3( 1113857

4lb minus l2ambg


4lb minus l2ambg

(10)

where

la l1 minus l2( 1113857 + l1 + l3( 1113857 + l1 + l4( 1113857

lb l1 minus l2( 11138572

+ l1 + l3( 11138572

+ l1 + l4( 11138572

(11)

(e static forces of each suspension are described asfollows

F1zsij 1

2F1zsi

(12)

(en the static vertical load of each wheel is described asfollows

F1zwij 1

2F1zsi

+ mwijg (13)

where mwij is the mass of each electric wheel(e dynamic force of suspension caused by a change in

the body posture is mainly reflected in the vehicle loadtransfer caused by the movement of the vehicle and the pitchmotion (e dynamic suspension force expression is asfollows

F2zsij Ksij zwij minuszsij plusmn Db

2 sinempty plusmn li sin θ1113888 1113889

+ Csij _zwij minuszsij plusmn Db

2empty_ cosempty plusmn li_θ sin θ

1113888 1113889

(14)

(e vertical movement tilting movement and pitchingmovement of the body lead to the vertical deformation of thesuspension expressed as follows

eurozsij eurozb plusmn Db

2emptymiddotmiddot plusmn liemptymiddotmiddot (15)

(e dynamic vertical force of the wheel caused by theunevenness of the pavement is as follows

F2zwij Kwij zij minus zwij1113872 1113873 + Cwij _zij minus _zwij1113872 1113873 (16)

(e suspension system and the vertical load of the tirecan be expressed as follows

Fzsij F1zsij + F2zsij

Fzwij F1zwij + F2zwij(17)

where zwij and zsij are the vertical displacement of thevertical position and the vertical displacement of the sus-pension system respectively Kwij and Cwij are the corre-sponding K and C tire characteristics and Ksij and Csij

denote the K and C characteristics of the suspension

23 Wheel Model Based on the dynamic analysis of wheelsin automobile theory [26] the differential equation for wheelmotion can be written as follows

Iwij _ωwij Twheelij minusTfij minusFxwijRwij (18)

where Twheelij Iwij ωij and Rwij represent the electric wheeltorque the moment of inertia the angular velocity and theeffective radius of the tire respectively

Tfij FzwijΔij FzwijfrRw (19)

where Tfij is the tire rolling resistance moment and Fzwij

and fr correspond to the vertical force of the wheel and therolling resistance coefficient

24 Tire Model Tires have strong nonlinear characteristicswhich are mainly manifested in the relationship between thelateral force and the cornering angle of the tire and therelationship between the lateral force and the longitudinalforce of the tire It is important to establish a tire model thatcan reflect the nonlinear characteristics of vehicle tiresCurrently the ldquomagicrdquo tire model power exponential uni-fied tire model and swift tire model are commonly used intire modeling In vehicle dynamics research the widely usedldquomagicrdquo tire model established by Professor Pacejka [32]based on test data and formula obtained by trigonometricfunction fitting can be used to completely and accuratelydescribe laterallongitudinal forces (e ldquomagicrdquo tire modelis more suitable for multiwheeled vehicles of large mass andhigh centroid and it is often used in multiaxle vehicle tiremodeling this model is used in the tire modeling of the8WIDEV (e tire model based on exact mathematicalformulas clearly describes changes in the tire longitudinalslip ratiolateral forces with changing tire slip ratioside slipangle (e longitudinal force and lateral force are obtainedby considering the influence of the ground adhesion co-efficient by modifying the basic expressions (eir specificdescription is given as followsFxij μDx

middot sin Cxarctan Bxλxij minusEx Bxλxij minus arctan Bxλxij1113872 11138731113872 11138731113960 11139611113966 1113967

Fyij μDy

middot sin Cyarctan Byαyij minusEy Byαyij minus arctan Byαyij1113872 11138731113872 11138731113960 11139611113966 1113967

(20)

where μ denotes the ground adhesion coefficient λxij andαyij are the corresponding longitudinal slip rate and side slipangle of the corresponding tire respectively and Bxy CxyDxy and Exy are gated by the fitting parameters of the tiremodel


Another way to express the longitudinallateral tire forceand the tire slip rateside slip angle is shown in Figure 4Figure 4 shows the relationship between the tire force and theslip rate clearly and is accurately expressed by the magicformula tire model Figure 4 shows the tire longitudinal forceand tire lateral force with respect to the tire slip rate when thetire vertical load is 4 kN and the road adhesion coefficient is 08(e red solid line black dashed line and black dashed line inFigure 4 represent the results at three different tire cornersrespectively (e three groups of lines that first increase andthen decrease are the result of the change of tire longitudinalforce with tire side slip angle while the remaining three groupsare the result of the change of tire lateral force with the tire sliprate Taking the red solid line as an example when the slip angleof the tire is 08 and the slip ratio of the tire is less than 02 therelationship between the longitudinal force of the tire and thecornering angle is almost linear and the tire longitudinal forceincreased with the slip rate And when the slip rate is 02 thetire longitudinal force reaches the maximum value When thetire slip rate continues to increase the longitudinal force de-creases nonlinearly with the tire slip rate (e tire lateral forcedecreases nonlinearly with the increase of the tire slip rateWhen the side slip angle of tire is the other value the tire forcehas similar analysis results with the change of the tire slip rate Itcan also be seen that at the same slip rate such as 02 the biggerthe side slip angle the larger the longitudinal force of the tireand the smaller the lateral force of the tire

25 Electric Motor Model (e parameter matching andselection requirements of in-wheel motors are decided bythe power and torque of the vehicle dynamics performanceIt is important to describe the process of choosing motorspecification based on the vehicle dynamics (e full load ofthe vehicle is tens of tons and considering the relatively largeavailable space for the hub a planetary gear reducer for thedrive system was selected with a transmission ratio preset as10 Next the choice of motor specification was divided intotwo parts the motor power demands and the motor torqueand speed requirements First we introduce the powerdemands of the motor (e motor power depends on thevehicle power demand Equation (21) expresses the vehiclepower demand

Pt Ff + Fw + Fi + Fj1113872 1113873vx

1000η (21)

where η is the mechanical transmission efficiencyBased on the vehicle dynamics performance the vehicle

power demand mainly concerns three aspects (1) the re-quirements for achieving maximum speed (2) achieving themaximum gradability performance and (3) satisfying theacceleration performance requirements of the vehicle (evehicle maximum speed is the top speed on a straight andgood road with full load or half load In this case the sloperesistance and acceleration resistance are zero (e vehiclepower demand can be obtained as follows

Pvmax Fi + Fw( 1113857

vmax

1000η (22)

where vmax and Pvmaxare the vehicle maximum speed and

maximum power under the maximum speed demanding

situation (e climbing ability of the vehicle is determinedsuch that all the power overcomes the slope resistance afterovercoming the rolling resistance Moreover the vehicle canmaintain a uniform speed

Pi mgf cos αs + sin αs( 1113857 +12

CDAjρv2i1113876 1113877

vi

1000η (23)

where αs and vi are the maximum gradient and the steadyspeed in this case and Pi is the vehicle power demand whenrealizing the maximum gradient (e maximum power Pa

should enable the vehicle to reach 50kmh in 50s (ereforethe vehiclersquos maximum power demand and rated powershould not be less than 1019 kW and 526 kW respectivelyNote that some in-wheel motors cannot effectively providepower in situations whereby the motor cannot functionnormally or whereby the vehicle is on a slippery or unevenroad Finally the required rated power of eachmotor is no lessthan 87 kW

Second we calculate the motor torque and speed re-quirements (e maximum speed and rated speed of thewheel motor are decided by the maximum speed andcommonly used speed respectively (e maximum speedand rated speed of the motor can be calculated as follows

n vx

0377Rwio (24)

(e maximum speed nmax 4420 rmin and the ratedspeed nmax 2652 rmin are calculated (e peak torque ofthe selected in-wheel motor is determined by the dynamicfactor of the vehicle

Tmax DMgR

zio (25)

where Tmax D and z are the peak torque of the motor thedynamic factor and the number of in-wheel motors (epeak torque is 992 kW when all eight motors are operatingproperly (e rated torque of the motor is determined by the

0 20 40 60 80 100Slip ratio ()

0

500

1000

1500

2000

2500

3000

3500

Tire

forc

e (N

)

α = 3degα = 5degα = 8deg

Figure 4 Tire force under different conditions


rated speed and rated power (e following equation de-scribes their relationship

Te 9550Pe

ne

(26)

(e rated torque of the motor is not less than 315Nmafter calculation Permanent magnet synchronous motors(PMSMs) are used as in-wheel motors to meet the vehicleperformance requirements By analyzing the requirementsof vehicle dynamic performance the rated power of themotor is finally chosen as 90 kW and the rated torque is340Nm (e final selection of the motor specifications isshown in Table 2 (e PMSM is designed and manufacturedby the motor manufacturer based on the basic motor de-mands and requirements

After choosing the motor model the PMSM wasmanufactured A bench test of the PMSM was conductedin the laboratory and the calibration was performed asshown in Figure 5 (e PMSM is installed on the benchwhich is controlled by the on-off switch of the IGBTof thePWSM controller (e motor is calibrated by controllingthe voltage and output torque of the motor and recordingthe current Figure 6 shows the external characteristiccurve of the motor at peak power and rated power re-spectively and interprets the relationship between motortorque and motor speed

(e vehicle controller which contains the electric stabilitycontrol system sends the target torque command to themotor controller (e main research topic here is the vehiclecontrol strategy toward improving the vehicle handling sta-bility (e response speed of the PMSMs is high comparedwith the wheel dynamics thus the input and output of thismotor torque is described as a first-order system

G(s) Tmout

Tmin

1τms + 1

(27)

where τm represents the damping ratioA planetary reducer is adopted between the in-wheel

motor and the hub (us the output torque of the electricwheel is

Twij Tmijiijηij (28)

where ηij and iij are the transmission ratio of the reducer andthe efficiency of the mechanical transmission respectively

3 Control Structure

An electronic stability control (ESC) is proposed in thispaper for the object under study in this paper 8WIDEV toimprove the vehicle stability performance therein adoptinga hierarchical control structure A hierarchical controlstructure is suitable for over-driven electric vehicles asshown in Figure 7 which includes the upper controller andlower controller (e upper controller can be applied to in-wheel motor-independent drive electric vehicles with strongand complex nonlinearities (e generalized target forcessuch as the target lateral force and the target yaw momentcan be obtained by using nonlinear or linear methods (e

lower controller can fully utilize the overdrive of the in-wheel motors to realize the distribution of the generalizedforce for the torque of each in-wheel motor

(e hierarchical control structure is superior to thecentralized control structure in terms of control flexibilityand fault tolerance (erefore the commonly used hier-archical control structure is designed to control thehandling stability of the 8WIDEV (e upper controllermostly controls the vehicle speed and yaw angular speedVehicle handling stability can be improved at low speedand good working conditions (e lower controller re-alizes the distribution of each motorrsquos torque by usingdifferent distribution methods By reasonably and effec-tively allocating the torque control vehicles for each in-wheel motor the vehicle can track the reference pathpreferable (e ESC proposed in this paper fully utilizesthe hierarchical structure and improves it on this basis(e ESC includes a reference state generation controlleran upper-level vehicle controller and a lower-level optimalcontrol allocation controller as illustrated in Figure 8 (ereference state generation controller based on a 2-DoF modelis designed to obtain the reference side slip angle (e upper-level vehicle motion controller including a yaw momentsynthesis controller and a longitudinal motion controllerobtains the corresponding control objective force to meet thestability requirements of the vehicle during the movingprocess Because of the advantages of sliding mode controlthe upper-level vehicle controller fully utilizes its nonlinearcharacteristics this can help in establishing an accuratemathematical relation compared with fuzzy logic controland effectively mitigate chattering by selecting an appropriatesliding surface and linear saturation function Considering thevehiclersquos handling stability under comprehensive operatingconditions the side slip angle and yaw angular velocity of thecenter of mass are considered simultaneously in the lateralstability (e in-wheel motorrsquos torque distribution is realizedby the optimization-based control allocation method underthe constraints(e optimization control allocation includingthe minimum tire load rate and error approximate mini-mization function considers the friction circle constraint andthe motorrsquos external characteristic constraint therein usingthe weighted least square method (WLS) to improve thedistribution efficiency By optimizing and designing the upperand lower controllers the vehicle handling stability can besignificantly improved

31 Reference State Generation Controller (e most com-monly used reference model in vehicle dynamic control as

Table 2 Basic specifications of motor

Parameter ValueRated power 90 kWMaximum power 110 kWRated torque 340NmMaximum torque 1100NmRated speed 2600 rpmMaximum speed 50000 rpm


shown in Figure 9 is the linear reference model based on theidea of a traditional two-axle vehicle [12] is referencedynamic model can calculate the reference state of a vehicleaccording to the driver inputs

e research object in this paper adopts a mechanicaldouble front axle steering mechanism based on Ackermansteering theory e state equation of the double front axlesteering vehicle can be described as follows

Observer

PWSM controller

In-wheel motor

Figure 5 PMSM calibration and debugging diagram

0 1000 2000 3000 4000 5000 6000Rotation speed (rmin)

0

200

400

600

800

1000

1200

Torq

ue (N

m)

Maximum power 110kWRated power 90kW

Figure 6 External characteristic curve of the PWSM

Longitudinal motion

controllerLateral stability

controller

Hierarchical control structure

Upper controller

Driver inputPedal signalSteering wheel angle

(1)(2)

Estimated signalsor measured signals

Vehiclemodel

Tire force distributioncontroller

Lowercontroller

8WIDEV

Figure 7 Traditional typical control structure for the 8WIDEV


_β

_ωz

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

minus2 C1 + C2 + C3 + C4( 1113857

Mvx

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Mv2xminus 1

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Iz

minus2 l21C1 + l22C2 + l23C3 + l24C41113872 1113873

Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

β

ωz

⎡⎢⎣ ⎤⎥⎦ +

2C1

Mvx

2C1l1Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

δ1 (29)

where C1 is the lateral stiffness of each axle M denotes thevehicle weight when fully equipped and Iz is the z-axismoment of inertia

(e ground adhesion vehicle limits the maximum lateralacceleration thus the maximum yaw rate is limited by themaximum lateral acceleration and the longitudinal speed

δ2v2

α2

Fy2

y

V δ1α1v1

Fy1Fy3Fy4

α4 α3

l1

l2l3

l4

x2 134

Figure 9 2DOF linear bicycle model

Driverinputs

2 DOF dynamic

model

Yawmomentsynthesiscontroller

Speedtracking

controller

Motorcontroller

3L

2R

2L

1R

1L

3R

4L

4R

8 in-wheel motor drive

electric vehicle

δfTlowast

1L

Tlowast

1R

Tlowast

2L

Tlowast

2R

Tlowast

3L

Tlowast

3R

Tlowast

4L

Tlowast

4R

T1L

T1R

T2L

T2R

T3L

T3R

T4L

T4R

ddt

ddt

Mzxminusωzdes

vd +

v

ωz

ωzdes +

+

ax

Mzxminusβdes

Mzxdes

ωzdes

βdesMzxdes

δ micro

Xxdes

ωz β

Fzij

Xxdes

βdes

β

Fxwij

Sliding modecontrol

Sliding modecontrol

Reference stategenerationcontroller

Upper-levelvhicle motion

controller

Lower-level optimalcontrol allocation

controller

Tire force

Actuator torque

Torquedistributionalgorithm

Sliding modecontrol

Weightedcontrol

Figure 8 Control structure for 8WIDEV


Similarly satisfying the vehicle lateral safety the side slipangle is subject to the longitudinal speed [26]

ωzd leμg

vx

βd le 10deg minus 7degv2x

(40ms)2

(30)

Based on the above analysis the vehiclersquos two idealvariables are described by the following equation

ωzdes min ωzdωd( 1113857sgn δ1( 1113857

βdes min β βd( 1113857(31)

In a sense to simplify the algorithm it is assumed thatthe vehicle acceleration and the displacement of theacceleratorbrake pedal are linear (us the expected speedof the vehicle is obtained

vxdes vo + 1113946t

to

ax(τ)dτ (32)

where vo is the initial vehicle longitudinal velocity at time to

and ax denotes the desired longitudinal accelerationdeceleration

32 Upper-Level Vehicle Controller (e upper-level vehiclecontroller contains the vehicle longitudinal motion con-troller and the vehicle yaw motion synthesis controllerwhose purpose is to generate the objective longitudinal forceand the objective yaw moment of the vehicle as needed Bytracking the longitudinal speed the vehicle longitudinalmotion controller obtains the desired longitudinal force(eside slip angle as another variable is controlled to obtain theobjective yaw moment instead of obtaining the lateral forcerequired by the vehicle which reduces the saturation of thetire longitudinal force distribution due to the lateral forcerequired by the vehicle (e vehicle yaw moment synthesiscontroller obtains the synthetic moment by controlling theside slip angle and the yaw rate

Vehicle handling stability is mainly determined by thelongitudinal speed and yaw rate According to the deviationfrom the reference state and actual state the desired lon-gitudinal force Xdes produced by the tire longitudinal andthe lateral forces Ydes are calculated Using the samemethodthe desired lateral force and the desired yaw moment Mzdescan be obtained (e upper-level vehicle controller isdesigned using differential equations (1) (2) and (6) (esimplified differential equation is expressed as follows

m _vx minus vyωz1113872 1113873 Xdes minusf

mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)

where f represents the sum of the air resistance slope re-sistance and rolling resistance

(e tire force control is realized by the actuator Becauseof the nonlinear coupling between the longitudinal andlateral forces the actuator faces difficulties in controlling the

lateral force accurately Moreover the output torque of themotor and brake directly affects the longitudinal force of thetire (e vehicle studied in this paper does not utilize activesteering thus it is difficult to control the lateral force ac-curately by compensating with the steering angle

In this paper the resultant force and yaw momentproduced by the tire longitudinal force are taken as the targetcontrol force

Xxdes Xdes minusXydes

Yxdes Ydes minusYydes

Mzxdes Mzdes minusMzydes

(34)

where

Xydes 1113944

4

1Fywil sin δij + Fywir sin δij1113872 1113873

Yydes 11139444

1Fywil cos δij + Fywir cos δij1113872 1113873

Mydes bi 1113944

4

1Fywil sin δij minusFywir cos δij1113872 1113873

+ 11139444

1li Fywij + Fywij1113872 1113873

(35)

in which Xydes Yydes and Mzydes are the reference longi-tudinal force lateral force and yaw moment of the vehiclegenerated by every tire lateral force Xxdes Yxdes and Mzxdesare the corresponding forceyaw moment of the vehicle bythe longitudinal force of the obtained tire vectordecomposition

Because of its strong robustness and anti-interferenceability sliding model control (SMC) is adopted in this paperto address the vehicle nonlinearity unmodeled dynamicsand parameter uncertainty [28] (e fundamental aspect ofthe sliding surface design is to make the vehicle track theobjective of the longitudinal speed side slip angle and yawrate (e sliding surface is selected as follows

Svx vx minus vxdes

sβ βminus βdes

sωz ωz minusωzdes + κ1113946 ωz minusωzdes( 1113857dτ

(36)

where Svx sβ and sωz

are the sliding surface and κ is theintegral coefficient (e control error gradually weakens ordecreases to zero as si approaches zero (e switchingfunction can be used to improve the quality of the slidingmode motion as can the proper selection of the reachinglaw (e constant velocity reaching law is adopted in thispaper It can be described by the following equation

_svx minusεusign su( 1113857

_sβ minusεβsign sβ1113872 1113873

_sωz minusεωz

sign sωz1113872 1113873

(37)


where εu εβ and εωzare the approaching law constant (e

yaw moment is not directly related to the vehicle side slipangle and therefore an intermediate variable is constructed(e intermediate control variable is obtained by the fol-lowing equation

ωzminusβ Ydes

mvx

minus _βdes + εβsign sβ1113872 1113873 (38)

(us the sliding mode function and the approach laware further expressed as follows

sωminusβ ωz minusωzminusβ

_sωminusβ minusεωzminusβsign sωzminusβ

1113874 1113875(39)

In the sliding mode control law we use the Lyapunovstability theory to design an appropriate sliding modecontrol to satisfy the reachability condition (e Lyapunovfunction is constructed as follows

Vi 12s2i (40)

(is represents the distance from the system curve to theswitching function and the Lyapunov inequality is describedas follows

_Vi si _si minussiεisign sωzminusβ1113874 1113875le εi si

11138681113868111386811138681113868111386811138681113868 (41)

As long as the Lyapunov arrival condition is satisfied themoving points outside the sliding mode will reach thesurface in a finite time approaching to the sliding surface(us the inequality εi gt 0 should hold To mitigate chat-tering caused by the switching of system state values near thesliding mode surface the linear saturation function takes theplace of the sign function as in the following equation

satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)

(rough equations (34)ndash(42) the objective referencelongitudinal force and the objective yaw moment given thegeneralized target force to be obtained are obtained

Xxdes minusXydes + m _vx minus εvxsat

svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f

Mzxminusβdes minusbiYdes + Iz ωzminusβ minus εωzminusβsat sωzminusβ

1113874 11138751113876 1113877

Mzxminusωzdes minusMzydes + Iz

middot _ωzdes minus εωzsat

sωz

Δωz

1113888 1113889minus κ ωz minusωzdes( 11138571113890 1113891

(43)

where Mzxminusβdes and Mzxminusωzdes are calculated by the corre-sponding actual variables tracking the ideal reference sideslip angle and the ideal reference yaw rate respectivelyHowever Mzxminusβdes is obtained by controlling the vehicle sideslip angle with ωzminusβ taken as an intermediate variable andtracking the ideal reference side slip angle

(e yaw moment synthesis controller obtains the ob-jective yaw moment though a joint action calculation resultthough two variables by adjusting the corresponding weightcoefficient [19]

Mzxdes K1Mzxminusωzdes + K2Mzxminusβdes (44)

where K1 and K2 are the weight coefficients of the yawmoment If the variation rate of the state quantity deviationis increased the corresponding weight coefficient increasesotherwise the corresponding weight coefficient decreases(e 8WIDEV can satisfy the stability control requirementsas long as the tire force satisfies the generalized force in thevehicle v Xxdes Mzxdes1113858 1113859

T in the lower-level controller

33 Lower-Level Optimal Control Allocation ControllerAs the most important part of the ESC system the lower-level controller plays a crucial role in the motor torquedistribution and manages the distribution of the longi-tudinal forceyaw moment acquired by the upper-levelvehicle controller (e force of each tire including thetire longitudinal force and the tire lateral force can becontrolled theoretically However the wheel steering angleis directly related to the input of the steering wheel driverand the 8WIDEV as the research object in this paper doesnot utilize active steering (e lateral force of the tire isdifficult to control accurately (erefore the resultantforce of the tire longitudinal force in the vehicle coordinatesystem is taken as the target force defined as v (e twodifferent torque distribution methods concretely speak-ing the rule-based braking torque distribution and opti-mization control allocation are described in the followingparts (e rule-based braking torque distribution isdesigned using the traditional DYC Correspondingly theESC proposed in this paper uses the optimization torqueallocation method (e two allocation methods are in-troduced in the following two sections

331 Rule-Based Braking Torque Distribution According tothe description of the vehicle steering in vehicle theory theeffect of each wheel generating a braking force on the yawmoment of the vehicle is different (e main contributionto the internal yaw moment of the vehicle comes from therear inner wheel whereas the lateral yaw moment pro-duced by the front inner wheel is the most effective [22]First we determine the value and direction of the yawmoment of the required motion Second the required yawmoment satisfies the requirements according to thebraking torque distribution Considering the differenteffects of each in-wheel motor on the yaw moment of thevehicle a rule-based braking torque distribution is pro-posed in this paper and as a contrastive control strategy


(e dynamic distribution ratios of power from the main tosecondary system are 05 025 015 01

During vehicle steering there are two cases of noteinsufficient steering and excessive steering Figure 10 showsthe case of insufficient steering during a left turn(e desiredyaw rate is nonnegative and larger than the actual yawmoment (eir expressions are given as follows

ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)

By comprehensively analyzing and compensating thelack of vehicle steering in this case the required yawmomentis found to be toward the inside the inner rear wheel is themain brake wheel and the other wheel on the left is thesecondary brake wheel (e left wheel force produces therequired yaw moment as follows

nablaMzb b Fb11 cos δ11 + Fb21 cos δ21 + Fb31 + Fb41( 1113857

minus l1Fb11 sin δ11 minus l2Fb21 sin δ21

st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)

where nablaMzb and Fbij are the additional yawmoment and thebraking force exerted by each motor respectively (e rulesfor the other cases including the excessive steering in the leftturn and excessive steering and insufficient steering in theright turn are the same as in the above case

332 Optimization Torque Distribution Actuator torqueallocation for redundant systems can be described as aconstraint optimization problem Considering the nonlinearsaturation and coupling relationship of the tire force andtorque saturation amplitude of the drive motor the lower-level optimal control allocation controller is constructed(e nonlinear tire is regarded as a more extensive ldquocon-strained nonlinear actuatorrdquo in the control allocation (eoptimization-based control allocation method-weightedleast square method (WLS) is introduced in this paperand can achieve the required vehicle stability performance[6]

According to equations (1)ndash(3) (7) and (8) the re-lationship between the objective force and the tire longi-tudinal force can be expressed by

Bu v (47)where

u Fxw11 Fxw12 Fxw21 Fxw22 Fxw31 Fxw32 Fxw41 Fxw421113858 1113859T

B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)

B and u denote the coefficient matrix and the output var-iable respectively

aij cos δij

bij (minus1)jd cos δij +(minus1)

ili sin δij

(49)

(e maximum tire longitudinal output force cannotexceed the tire friction ellipse constraint and externalcharacteristic curve of the motor torque First the tire forceis limited by the ground adhesion and the dynamic verticalforce of each tire According to the concept of the tirefriction circle the tire longitudinal force and lateral forceneed to satisfy the following conditions

minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)

where Tmmax Rw and ig are the maximum in-wheel motoroutput torque wheel radius and deceleration ratio of thereducer Second the friction circle coupled with the lon-gitudinal force and lateral force also limits the output tirelongitudinal force

Overall considering the friction circle constraint and themaximum torque constraint of the in-wheel motor theconstraint of the longitudinal force of the tire can be mergedinto the following equation

uij le uij le uij (51)

where

uij max

μijFzij1113872 11138732minusF2

ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)

(e constraint condition Bu v is an equality con-straint It is possible that there is no solution in the limitcondition To address this possible problem the minimumerror approximation Buminus v2 is used to replace the equalityequation constraint (e main goal of the optimal allocationis to minimize the allocation error (e objective equationcan be expressed by the squared norm

J1 argmin Wv(Buminus v)2 (53)

where Wv is the diagonal weighted matrix for adjusting thetracking performance It is defined as follows

Wv diag WvFx WvMz( 1113857 (54)

21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb

Figure 10 Rule-based braking torque distribution


To improve the vehicle stability by guaranteeing theoutput reserve of the tire longitudinal force the vehiclersquosstability margin is also considered when the vehicle torque isallocated (erefore considering further improvement inthe stability under the limit condition and maneuverabilityunder good conditions an additional objective function isused based on the principle of the small tire load rate byreserving the load of the longitudinal force Its norm ex-pression is expressed by the following condition

J2 Wuu2 (55)

where Wu means the diagonal weighted matrix(e distribution of the objective forcemoment obtained

by the upper-level vehicle controller into the longitudinalforce of each tire is an optimization-based control allocationproblem with a boundary constraint (is leads to a linearconstrained quadratic programming problem Such problemcan be expressed as follows

u argminWuu2 u le ule u

Ω argminWv(Buminus v)2

(56)

(is problem is typical of the two-step optimization ofsequential least squares (SLS) By setting the weight co-efficient c the above two-step algorithm can be integratedinto a one-step algorithm and solved by weighted leastsquare (WLS) [17]

(e active set method algorithm is used to calculate thetarget torque of the in-wheel motor as shown in Figure 11In the active set method it is important to calculate pk andjudge whether pk is zero Following this process the optimalsolution 1113954x of the constrained optimization objective canultimately be obtained

4 Vehicle Model Verification and Analysis ofControl Strategy

(e 8WIDEV developed by our lab is a modified 8times 8prototype vehicle whose basic structural parameters areshown in Table 1 Section 41 mainly concerns the com-parative analysis of the vehicle model simulation and vehicleexperiments under the same conditions and analysis of theESC in the hardware-in-the-loop simulation platform ispresented in Section 42

41 Vehicle Model Validation First we verify the effec-tiveness of the vehicle dynamic model built-in MATLABSimulink (e validity of the vehicle dynamic model can beapproximately verified by comparing the prototype vehicleresults with the simulation results of the dynamics model ofthe 8WIDEV under different and the same conditions (eexperimental vehicle is equipped with gyroscopesacceleratorbrake pedal signal sensors and a steering wheelangle sensor and is driven by eight in-wheel motors withequal torque

(rough comparison of the experimental vehicle testdata and simulation of the vehicle model the accuracy of themodel is verified Under this scheme deviations between the

torque values obtained by each wheel and those of the wheelsin the prototype vehicle are unavoidable However underthe premise of sufficient power and satisfying the givenvehicle working conditions the influence of the deviationson the handling stability is not significant

(e vehicle angle step input and snake condition test aretypical conditions for testing vehicle dynamics and are alsoimportant conditions in testing vehicle handling stability(erefore the two conditions are utilized based on con-trollability and stability test procedures for automobi-lesmdashthe Pylon course slalom test of GBT 63231-1994mdashtocompare the results of the experimental vehicle and thesimulation results of the vehicle model (e vehicle modelestablished in MATLABSimulink uses the built-inMATLABSimulink DormandndashPrince algorithm to solvethe problem

Figure 12 shows the experimental 8WIDEVwith angularsteps at the laboratory site of a cooperating companyFigure 1 shows the experimental vehicle with angular steps atthe experimental site In the steering wheel angle step inputcondition the longitudinal speed is set to a constant value of80 kmh Figure 12 describes the results of the prototypevehicle results and the 8WIDEV simulation including the(a) steering angle (b) yaw rate (c) lateral acceleration and(d) body roll angle Figure 12(a) shows the comparison of thedata collected from the steering wheel angle sensor and thesimulation results from MATLABSimulink

(e simulation results reach their maximum in a veryshort period of time and remain unchanged for a typicalangular step change of 2 seconds In contrast the experi-mental vehicle was slightly delayed however it also com-pleted a step change in 04 seconds and remainedunchanged Both vehicles ended up at 57 degreesFigure 12(b) shows the comparison results of the vehicle yawrate under experimental and simulation conditions(e finalsteady-state value of the vehicle simulation and experimentalresults is approximately 58 degs In addition throughcomparative experiments it is found that the time forsimulation stabilization in MATLABSimulink is 03 s fasterthan that in the experimental vehicle experimentFigure 12(c) shows the results of the changes in the lateralacceleration of the vehicle dynamics (e lateral accelerationof the vehicle increases gradually from zero at 2 s to 2ms2 inthe 34 s (e lateral acceleration of the experimental vehiclewas stabilized at 2ms2 at 36 s which shows a delay of 6compared with the simulation results (e amplitude in thesimulation results is slightly larger than that in the exper-imental results Figure 12(d) shows the changes in the rollangle of the vehicle of vehicle dynamics It also produces thesame analysis results as the lateral accelerationFigures 12(b)ndash12(d) show that the steady-state values of theyaw rate lateral acceleration and roll angle and their cor-responding times are approximately equal (ere is a slightdifference between experiment and simulation in terms oftransient response with the stepped input of the samesteering wheel angle

(e vehicle during the snake experiment passes throughfour piles at a constant speed of 50 kmh Figure 13 shows the8WIDEV performing the snake experiment at the


experimental site Figure 14 displays the simulation results ofthe vehicle dynamics model and the results of the prototypevehicle including the (a) longitudinal and lateral displace-ment (b) longitudinal speed (c) steering wheel angle (d)yaw rate and (e) roll rate and lateral velocity

(e solid line in Figure 14 represents the simulationresults in MATLABSimulink while the dotted line repre-sents the experimental results of the experimental vehicleFigure 14(a) shows the trajectory of the 8WIDEV in geodeticcoordinates (e maximum lateral displacement of the8WIDEVmodel simulation is 47m which is larger than themaximum lateral displacement of the experimental vehicleby 45m (e error is less than 5 when comparing theirtrajectories Figure 14(b) shows the longitudinal speedchanges over time (ese changes basically stabilized at afixed speed of 50 kmh In addition the lateral motion of thevehicle caused fluctuations of the vehicle longitudinal speedwhere the maximum fluctuation value was not more than2ms2(e vehicle is turning at the maximum steering wheelangle of 200 deg as described in Figure 14(c) (e yaw ratemaximum was 20 degs during maximum lateral displace-ment as illustrated in Figure 14(d) Figures 14(e) and 14(f)show that the roll angle and lateral acceleration follow thesame rule (e results of MATLABSimulink simulation areconsistent with the results of the experimental 8WIDEV Bycomparison each index response process of the simulationof the vehicle dynamics model built-in MATLABSimulinkand the results of the experimental prototype are the same

(rough the simulation test and real vehicle test of the8times 8 prototype vehicle the response speed of the vehicle

model is found to be related to the real vehicle test(emainreason for this is that the simulationmodel does not considerthe characteristics of free travel inertia and stiffness of thesteering system and there are differences between the actualdriverrsquos operation and an ideal driverrsquos operation in thesimulation model In terms of response amplitude thedeviation between the simulation results and the real vehicletests is large at the peak mainly because the simulationmodel neglects the inertia of certain rotating parts in the realvehicle and simplifies the suspension system to be a mass-free fixed stiffness and fixed damping object In additionthe accuracy of the tire model also produces deviations fromthe test results However these deviations are essentiallyunavoidable Generally the test results are consistent interms of their trend and the deviations between the resultsare within a reasonable range (erefore from a practicalpoint of view the simulationmodel can accurately reflect theresponse characteristics of the real vehicle From a theo-retical point of view the accuracy of the simulation modelcan satisfy the requirements of vehicle dynamics researchand can be used as a simulation model for vehicle handlingand stability control

It is demonstrated that the vehicle model based onMATLABSimulink can reflect the dynamic characteristicsof the 8times 8 prototype vehicle (e errors between the vehiclemodel and experimental vehicle remain as less than 8(isis sufficient to show that the vehicle model can replace theexperimental 8WIDEV for simulation experiments therebyproviding a favorable basis and conditions for the validationof the control strategy of handling stability

Start

Yes

No

Yes

No

End

Initialize i j x0 W0 k = 0

k gt i + j

k = k + 1 calculate pk

pk = 0

ˆ ˆW = Wk x = xcalculate λi

ˆλi (i isin W) gt= 0 iisinWkcapIik = arg min λi

xk+1 = xk Wk+1 = Wkik

αk (ik notin Wk) lt 1

Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1

Figure 11 (e active set method algorithm


42 Analysis and Comparison of Proposed Control Strategy(is section mainly verifies the ESC proposed in this paperBecause the test prototype vehicle is still in the debuggingstage it is not possible to verify the ESC proposed in thispaper on the experimental vehicle driven by 8 in-wheelmotors developed by our lab To verify the ESC strategyproposed in this paper a hardware-in-the-loop (HIL) test

platform based on dSPACEAutoBox is built by the authors(e HIL platform includes a ACDC inverter dSPACEAutoBox VCU brakeaccelerator pedal steer wheel CANbus and related accessories

Figure 15 shows a process schematic of the HIL platform(e VCU includes the ESC strategy code automaticallygenerated by the real-time workspace (RTW) provided byMATLABSimulink and the manual code integration isconducted in CodeWarrior (e necessary hardware-relatedcodes such as the header file interrupt service program andhardware-related codes are included (e ESC strategy istransformed into a real-time code in this way (e vehicledynamic simulation model is embedded in dSPACEAutoBox in the form of a real-time simulation modelFirst the RTW real-time code generation environmentprovided by MATLABSimulink is used to automaticallygenerate real-time code for the vehicle dynamic simulationmodel (en the real-time code of the vehicle dynamicsimulation model is downloaded to the AutoBox real-timesimulator by using the Real-Time Interface (RTI) provided

0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)

ExperimentSimulation

(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)

Figure 12 Step input condition results (a) steering wheel angle (b) yaw rate (c) lateral acceleration (d) roll angle

Figure 13 8WIDEV experiment at the test site


0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )

Figure 14 Snake condition results (a) trajectory (b) longitudinal velocity (c) steering wheel angle (d) yaw rate (e) roll angle (f ) lateralvelocity


by dSPACE such that the AutoBox is equivalent to theldquoexperiment vehiclerdquo that can operate in real time (einformation exchange and interconnections between theVCU and dSPACEAutoBox are realized by the CAN bus(e PC interacts with dSPACEAutoBox through theControlDesk test kit for eg adjusting parameters onlinedisplaying the status of the control system and data storageand tracking the response curve of the process

(e above introduced the construction of the HILsimulation platform(e construction of the test bed mainlyconcerns the process and theory of building the HIL sim-ulation platform (e completed HIL simulation platform isshown in Figure 16 (e specific experimental process isgiven below

During the test the driver inputs the driving intentinstructions to the VCU through the AD interface (evehicle controller filters and calibrates these signals linearlyfor the accelerationbrake pedal and steering wheel sensorsignals which are converted into digital signals Based onthese signals and the real-time vehicle status feedback suchas the in-wheel motor working status and the wheel angle ofdSPACEAutoBox the real-time operation control algo-rithm is implemented and control instructions are sent todSPACEAutoBox for real-time control

Simultaneously the AutoBox DS1005 processing boardreceives the in-wheelmotor torque command sent by theVCUand runs the vehicle dynamic simulation model in real timethrough the real-time control module(e real-time change ofthe vehicle state value and the in-wheel motor state value arefed back to the monitoring interface of the ControlDesk andPC (e measurement control parameter adjustment andmonitoring interface based on the ControlDesk integratedtesting software can interact with the vehicle motion pa-rameter signals and driving environment information

(e double-line simulation with a driver-in-loop setup isa classic test condition for vehicle stability testing thistesting type is selected in this paper and sets a constantlongitudinal vehicle speed of 100 kmh (e purpose of thehigh-speed setting is to conduct investigations and evaluatethe stability performance of the vehicle (e DYC methodbased on the hierarchical control structure utilizes the samereference model and upper controller as the ESC (e dif-ference between them is that the DYC method uses theproposed method in Section 331 in the lower controllerwhereas the ESC uses the optimization torque distribution inthe lower controller

Figure 17(a) describes how the vehicle trajectory con-trolled by the two methods can track the desired trajectory

Vehicle model

ESC model

Simulink

AutoBox

Driversignals

Model codedownload CAN bus

TCPIP

PC

HIL

VCU

Figure 15 Schematic process of the HIL system

ACDC

ControlDeskinterface

VCU

Pedel

dSPACEAutoBox

CAN bus

Figure 16 Hardware-in-the-loop test platform


and the ESC strategy achieves good performance in tra-jectory tracking compared with the DYC It can also be seenthat the trajectory controlled by the DYC cannot track thedesired path well in the second section of the straight linebecause the actual path cannot converge quickly to thedesired path description and there is a certain amplitudeof left-right swing along the desired path FromFigure 17(b) the longitudinal speed is approximatelystable at the expected velocity and can track the expectedspeed under the ESC system proposed in this paper Inaddition the longitudinal speed controlled by the DYC islower than the expected speed in the lane-change processand shows a small fluctuation Two variables can becontrolled under the DYC and ESC in Figures 17(c) and17(d) (e yaw rate and side angle of the vehicle in the laststraight line oscillate slightly and it requires approxi-mately 3 s to stabilize Figure 17(e) shows that the tra-jectories in the phase diagrams of the two control methodscan converge to zero (is proves that the two controlmethods are effective at ensuring vehicle stability which isconsistent with Figure 17(a) (e phase diagram of the sideslip angle and side slip angle rate is an important basis forjudging vehicle stability Figure 17(f ) also proves this pointbecause the error of the expected yaw rate and the actualyaw rate is smaller when controlled by the optimizationmethod (e proposed method and DYC can guaranteeproper vehicle handling and stability at high speed from

the vehicle kinematics analysis In addition the ESC basedon optimal control has a faster tracking performance andgreater stability compared with the DYC based on the rule-based braking torque distribution

Figures 18(a) and 18(b) show the eight in-wheel motortorque distribution of the ESC Figure 18(a) shows the frontfour in-wheel motor drivingbraking torque whileFigure 18(b) shows the rear four in-wheel motor drivingbraking torque Figures 18(c) and 18(d) both describe theeight in-wheel motor torques controlled by the DYC (eoptimal output change rate of the in-wheel motors con-trolled by the ESC is small in contrast to the DYC dis-tribution Based on the optimal control method theutilized maximum negative and positive torques of themotor of the ESC are minus100 Nm and 200Nm (e motoralmost operates in the rated torque range and fully utilizesthe independent control of each motor (e DYC based onthe rule-based braking torque distribution is essentiallydifferent from the control methods proposed in this paperand realizes the stabilization of the vehicle by applyingbraking torque to the motors after the torque distribution isdetermined (erefore when the braking torque is appliedthe negative motor torque readily saturates such that thepeak torque of the motors can be easily reached (ebreaking torque of the left first and left third in-wheelmotors already exceeded minus330Nm which negatively affectsvehicle handling and stability

0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC

ndash5 0 5Side slip angle β (rad)

ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )

Figure 17 HIL simulation results (a) trajectory (b) longitudinal speed (c) yaw rate (d) side slip angle (e) side slip angle change rate(f ) side slip angle and its rate


5 Discussion and Conclusions

Each in-wheel motor is independently and precisely con-trolled making the system more likely to achieve vehicledynamic stability control (e ESC proposed for an8WIDEV improves the vehicle handling and control sta-bility A hierarchical top-down control structure includes areference state generation controller an upper-level vehiclecontroller and a lower-level optimal control allocationcontroller (e upper-level vehicle controller including theyaw moment synthesis controller comprehensively con-siders the objective yaw moment calculated from the errorof the side slip angle and the error of the yaw rate byadjusting the weight coefficient (e lower-level optimalallocation controller based on an accurate control alloca-tion method takes not only the friction circle constraint ofthe mutual coupling of the tire longitudinal forcelateralforce and external characteristic constraint of the in-wheelmotor into account but also utilizes an advanced fastcalculation method WLS for the torque distribution ineach in-wheel motor (e effectiveness of the vehicle dy-namic model based on prototype parameters is verified by

comparison under two different conditions (e validity ofthe vehicle dynamic model established in this paper isverified by comparing simulation and experiment resultsIn addition the HIL experimental results confirmed thatthe ESC proposed in this paper compared with the DYCcan improve the handling and control stability of the ve-hicle Each motor has two different working modes whichcan coordinate generating the desired yaw moment Bothsimulation results and experimental results have shownthat the transient response speed of the vehicle is high

Our next task is to apply the ESC proposed in this paperto the experimental vehicle after completing debugging andverifying the ESC control strategy More importantly the in-wheel motor more effectively enables the regeneration ofenergy to the battery during braking and thus increases thevehiclersquos range which is another hot topic and directionworth studying

Data Availability

(e data used to support the finding of this study areavailable from the corresponding author

0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)

Figure 18 HIL simulation results (a) ESC torque distribution of front four wheels (b) ESC torque distribution of rear four wheels (c) DYCtorque distribution of front four wheels (d) DYC torque distribution of rear four wheels


Conflicts of Interest

(e authors declare that there are no conflicts of interest

Acknowledgments

(e research funding for this paper comes from a grant fromthe Chinese PLA General Armament of Department (no40402050101) (is project funding support is gratefully ac-knowledged and laid the foundation for this paper to proceedsmoothly

References

[1] X Jin G Yin X Zeng and J Chen ldquoRobust gain-scheduledoutput feedback yaw stability control for in-wheel-motor-driven electric vehicles with external yaw-momentrdquo Journal ofthe Franklin Institute vol 355 no 18 pp 9271ndash9297 2018

[2] Z Li L Zheng and W Gao ldquoCoordinated motion andpowertrain control of a series-parallel hybrid 8 times 8 vehiclewith electric wheelsrdquo Mechanical System and Signal Pro-cessing vol 120 pp 560ndash583 2019

[3] Z Li L Zheng W Gao and Z Zhan ldquoElectromechanicalcoupling mechanism and control strategy for in-wheel-motor-driven electric vehiclesrdquo IEEE Transactions on In-dustrial Electronics vol 66 no 6 pp 4524ndash4533 2019

[4] Z Yu Y Feng and L Xiong ldquoReview on vehicle dynamicscontrol of distributed drive electric vehiclerdquo Journal of Me-chanical Engineering vol 49 no 8 pp 105ndash114 2013

[5] D Tan Q Wang and Y Wu ldquoModal analysis of in-wheelmotor-driven electric vehicle based on bond graph theoryrdquoShock and Vibration vol 2017 Article ID 6459154 9 pages2017

[6] Y Wang Z Wang L Zhang M Liu and J Zhu ldquoLateralstability enhancement based on a novel sliding mode pre-diction control for a four-wheel-independently actuatedelectric vehiclerdquo IET Intelligent Transport Systems vol 13no 1 pp 124ndash133 2019

[7] M Doumiati O Sename L Dugard J J Martinez-MolinaP Gaspar and Z Szabo ldquoIntegrated vehicle dynamics controlvia coordination of active front steering and rear brakingrdquoEuropean Journal of Control vol 19 no 2 pp 121ndash143 2013

[8] B Ren H Chen H Zhao and L Yuan ldquoMPC-based yawstability control in in-wheel-motored EV via active frontsteering and motor torque distributionrdquo Mechatronicsvol 38 pp 103ndash114 2016

[9] J Wang and R G Longoria ldquoCoordinated and reconfigurablevehicle dynamics controlrdquo IEEE Transactions on ControlSystems Technology vol 17 no 3 pp 723ndash732 2009

[10] Z Yu B Leng L Xiong Y Feng and F Shi ldquoDirect yawmoment control for distributed drive electric vehicle handlingperformance improvementrdquo Chinese Journal of MechanicalEngineering vol 29 no 3 pp 486ndash497 2016

[11] H Alipour M Sabahi and M B Bannae Sharifian ldquoLateralstabilization of a four wheel independent drive electric vehicleon slippery roadsrdquo Mechatronics vol 30 pp 275ndash285 2015

[12] M Liu J Huang and M Cao ldquoHandling stability im-provement for a four-axle hybrid electric ground vehicledriven by in-wheel motorsrdquo IEEE Access vol 6 pp 2668ndash2682 2018

[13] D Savitski D Schleinin V Ivanov et al ldquoImprovement oftraction performance and off-road mobility for a vehicle withfour individual electric motors driving over icy roadrdquo Journalof Terramechanics vol 69 pp 33ndash43 2017

[14] B Li A Goodarzi A Khajepour S K Chen and B LitkouhildquoAn optimal torque distribution control strategy for four-independent wheel drive electric vehiclesrdquo Vehicle SystemDynamics vol 53 no 8 pp 1172ndash1189 2017

[15] Y Wang F Kang T Wang and H Ren ldquoA robust controlmethod for lateral stability control of in-wheel motoredelectric vehicle based on sideslip angle observerrdquo Shock andVibration vol 2018 Article ID 8197941 11 pages 2018

[16] L Jin and Y Liu ldquoStudy on adaptive slid mode controller forimproving handling stability of motorized electric vehiclesrdquoMathematical Problems in Engineering vol 2014 Article ID240857 10 pages 2014

[17] Z Wang Y Wang L Zhang and M Liu ldquoVehicle stabilityenhancement through hierarchical control for a four-wheel-independently-actuated electric vehiclerdquo Energies vol 10no 7 p 947 2017

[18] F Li Z Chen Y Wu and R Liu ldquoLane departure avoidancecontrol for electric vehicle using torque allocationrdquo Mathe-matical Problems in Engineering vol 2018 Article ID1024805 10 pages 2018

[19] L Zhai T Sun and J Wang ldquoElectronic stability controlbased on motor driving and braking torque distribution for afour in-wheel motor drive electric vehiclerdquo IEEE Transactionson Vehicular Technology vol 65 no 6 pp 4726ndash4739 2016

[20] L Xiong G W Teng Z P Yu W X Zhang and Y FengldquoNovel stability control strategy for distributed drive electricvehicle based on driver operation intentionrdquo InternationalJournal of Automotive Technology vol 17 no 4 pp 651ndash6632016

[21] W Cao H Liu C Lin Y Chang Z Liu and A SzumanowskildquoCo-design based lateral motion control of all-wheel-independent-drive electric vehicles with network conges-tionrdquo Energies vol 10 no 10 p 1641 2017

[22] W Xu H Chen H Zhao and B Ren ldquoTorque optimizationcontrol for electric vehicles with four in-wheel motorsequipped with regenerative braking systemrdquo Mechatronicsvol 57 pp 95ndash108 2019

[23] M C Liu and C N Zhang ldquoDevelopment of an optimalcontrol system for longitudinal and lateral stability of anindividual eight-wheel-drive electric vehiclerdquo InternationalJournal of Vehicle Design vol 69 no 1ndash4 pp 132ndash150 2015

[24] Q Wang J Goyal B Ayalew and A Singh ldquoControl allo-cation for multi-axle hub motor driven land vehicles withactive steeringrdquo SAE International Journal of AlternativePowertrains vol 5 no 2 pp 338ndash347 2016

[25] L De Novellis A Sorniotti P Gruber and A PennycottldquoComparison of feedback control techniques for torque-vectoring control of fully electric vehiclesrdquo IEEE Trans-actions on Vehicular Technology vol 63 no 8 pp 3612ndash36232014

[26] J Ni J Hu and C Xiang ldquoControl-configured-vehicle designand implementation on an X-by-wire electric vehiclerdquo IEEETransactions on Vehicular Technology vol 67 no 5pp 3755ndash3766 2018

[27] W Chu Y Luo and F A Zhao ldquoDriving torque coordinationcontrol of distributed drive electric vehiclesrdquo AutomotiveEngineering vol 3 pp 185ndash189 2012

[28] Y Chen S Chen Y Zhao Z Gao and C Li ldquoOptimizedhandling stability control strategy for a four in-wheel motorindependent-drive electric vehiclerdquo IEEE Access vol 7pp 17017ndash17032 2019

[29] B-C Chen and C-C Kuo ldquoElectronic stability control forelectric vehicle with four in-wheel motorsrdquo International


Journal of Automotive Technology vol 15 no 4 pp 573ndash5802014

[30] U Kiencke and L Nielsen ldquoAutomotive control systems forengine driveline and vehiclerdquo Sensor Review vol 11 no 4p 1828 2015

[31] V I Utkin ldquoSliding mode control design principles andapplications to electric drivesrdquo IEEE Transaction on IndustrialElectronics vol 40 no 1 pp 23ndash36 2002

[32] E Kuiper and J J M Van Oosten ldquo(e PAC2002 advancedhandling tire modelrdquoVehicle SystemDynamics vol 45 no s1pp 153ndash167 2007


International Journal of

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Submit your manuscripts atwwwhindawicom

Comparing with the widely used model following controlthe stability of the vehicle is improved [3 8 16] A controlstrategy with an optimal target is proposed to improve theelectric drive vehicle dynamic stability and maneuver-ability In lower-level optimal control allocation control-lers an optimization algorithm is used to distribute themotor torque to achieve effective control [17 18] Based ona hierarchical control structure an ESC system suitable fora 4WIDEV is presented (ree levels of control logic aredesigned in the ESC system which contains a torquedistribution algorithm based on a minimum-objective-function to enhance the vehiclersquos stability [19] Fully uti-lizing the hierarchical structure a linear quadratic regu-lator control method is obtained by controlling the yaw rateto design the upper-level controller and a fast calculationmethod is used to achieve a fast motor torque distribution[20] Taking two variables reflecting the advantages anddisadvantages of the vehiclersquos lateral movement in themotion control unit the objective yaw moment is obtainedby fuzzy logic control However this method is highlydependent on engineering and a lack of control accuracy[21] A new control method is proposed based on modelpredictive control (MPC) theory to address the issues ofmultiple objectives with constraints which can maximizethe regeneration efficiency while maintaining the vehicledynamics [22] (ese methods focus on the vehicle torqueallocation but do not optimize the vehicle handling stabilityfor vehicle motion control

However fewer studies have focused on the 8WIDEVwith high weights As the number of driving wheels in-creases the 8WIDEV becomes applicable to more com-plicated driving conditions given its greater flexibility andmaneuverability To improve the 8WIDEV handling sta-bility the longitudinal dynamic control and lateral dy-namic control are constructed (e target lateral force andtarget yaw moment are obtained by controlling the twocorresponding vehicle variables in lateral control [23] Ahierarchical control allocation strategy is developed byconsidering the real-time performance of the control formultiaxle land vehicles equipped with independent drivingwheels [24] Because the vehiclersquos steering wheel angle isnot large the distribution of the motor torque needs tosatisfy the demanded lateral force of the vehicle and thetorque of the motor readily experiences a saturated am-plitude Vehicle stability control is mainly reflected in twovariables Vehicle handling stability is not only related tothe vehicle longitudinal speed but also directly related tovehicle yaw speed and side slip angle which is directlyrelated to the vehicle heading angle and determines theperformance of the vehicle trajectory tracking In additionalthough the two variables are controlled simultaneouslysometimes and the target yaw moment and lateral force areobtained the motor output torque readily becomes satu-rated for a vehicle without active steering [10 23] Based onnonlinear control theory a fuzzy logic method the yawmoment is obtained by controlling the lateral slip angle andyaw rate However it is not easy to establish precisemathematical relations for this control method and it ismore dependent on experience [21]

(e yaw rate is mathematically related to yaw momentthus it can be directly controlled However the re-lationship between the side slip angle and yaw momentrepresents an ldquoun-matching systemrdquo which can beexpressed as that the side slip angle being tracked to anideal stare quantity by controlling the yaw rate as an in-termediate variable however the actual yaw rate is notsufficient to track its reference value [25] (e requiredlateral force can be calculated via steering angle controland the expected yaw moment is obtained by fully utilizingthe yaw rate (is integrated control method can be usedby active steering vehicles [26] (e control configurationvehicle principle is structured to improve the flexibilityand performance of the structure layout Although thismethod can focus on the side slip angle control it is onlysuitable for steer-by-wire vehicles which presents limi-tations for use in vehicles without active steering orauxiliary steering

Most control allocation rules now adopt traditionalallocation methods such as average allocation and directcontrol allocation (ese methods are faster in calculatingthe torque distribution however their torque allocationmethod is simple (e vehicle dynamics constraints andthe optimization of the torque distribution need to be fullyconsidered [27 28] Considering the nonlinear saturationand coupling relationship of the tire force and torquesaturation amplitude of the drive motor a lower-leveloptimal control allocation controller is constructed Anonlinear tire is regarded as a more extensive ldquoconstrainednonlinear actuatorrdquo in the control allocation (eoptimization-based control allocation method withweighted least square (WLS) is used for the torque forcedistribution this can effectively increase the computationspeed [29]

In this paper ESC based on a hierarchical controlstrategy is established to enhance the performance of thehandling stability and trajectory capability of 8WIDEV(e hierarchical control structure includes the referencestate generation controller the upper-level vehicle con-troller and the lower-level optimal control allocationcontroller By utilizing the classic reference model of thevehicle a monorail of four-axle vehicles based on a twoDoF model is established to obtain the required referencestate of the vehicle (e reference state generation con-troller is designed using the reference state of the vehicleIn contrast to the linear control method attempting toconsider vehicle nonlinearity and uncertainty the upper-level vehicle controller is built using the nonlinear controlmethod therein achieving strong robustness to vehicleparameter uncertainties and external disturbances (eupper-level vehicle controller includes a yaw momentsynthesis controller therein considering the two controlvariables related to lateral motion tracking while adjustingthe weight coefficient Actuator torque allocation for re-dundant systems is modeled as a constrained optimizationproblem (e main contribution of this paper lies in thefollowing points First based on prototype vehicle pa-rameters a dynamic model of an 8WIDEV is established(is model can fully reflect the dynamic characteristics of




2 Vehicle Model





max 11139444


may 11139444

1Fyij1113872 1113873 (2)

mbaz 11139444

1Fzsij (3)



Ix _ωx di 1113944

4








1li Fyi1 minusFyi21113872 1113873 (6)











41 31 21 11

42 32 22 12

ωZ O

Fxw41

Fyw41

α41

v41

Fxw42

Fyw42

α42v42

Fxw31

Fyw31

α31

v31

Fxw32

Fyw32

α32v32

Fxw21

δ21α21

v21

Fyw21

Fxw11

δ11α11

v11

Fyw11

Fxw22

δ22α22

v21

Fyw22

Fxw12

δ12α12

v12

Fyw12

y

x

l1l4

l2l3

bi = 2divx

vyβ

V


Fxwij

Fywij

xw

yw

vwσ

α




F1zs1 lb minus lal1

4lb minus l2ambg


4lb minus l2ambg


4lb minus l2ambg


4lb minus l2ambg

(10)

where

la l1 minus l2( 1113857 + l1 + l3( 1113857 + l1 + l4( 1113857

lb l1 minus l2( 11138572

+ l1 + l3( 11138572

+ l1 + l4( 11138572

(11)


F1zsij 1

2F1zsi

(12)


F1zwij 1

2F1zsi

+ mwijg (13)







1113888 1113889

(14)



















Fyij μDy


(20)





Pt Ff + Fw + Fi + Fj1113872 1113873vx

1000η (21)




vmax

1000η (22)





CDAjρv2i1113876 1113877

vi

1000η (23)




n vx

0377Rwio (24)


Tmax DMgR

zio (25)


0 20 40 60 80 100Slip ratio ()

0

500

1000

1500

2000

2500

3000

3500

Tire

forc

e (N

)





Te 9550Pe

ne

(26)




G(s) Tmout

Tmin

1τms + 1

(27)





3 Control Structure










Observer

PWSM controller

In-wheel motor



0

200

400

600

800

1000

1200

Torq

ue (N

m)



Longitudinal motion


controller


Upper controller


(1)(2)


Vehiclemodel


Lowercontroller

8WIDEV



_β

_ωz

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

minus2 C1 + C2 + C3 + C4( 1113857

Mvx

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Mv2xminus 1

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Iz

minus2 l21C1 + l22C2 + l23C3 + l24C41113872 1113873

Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

β

ωz

⎡⎢⎣ ⎤⎥⎦ +

2C1

Mvx

2C1l1Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

δ1 (29)



δ2v2

α2

Fy2

y

V δ1α1v1

Fy1Fy3Fy4

α4 α3

l1

l2l3

l4

x2 134


Driverinputs

2 DOF dynamic

model


Speedtracking

controller

Motorcontroller

3L

2R

2L

1R

1L

3R

4L

4R


electric vehicle

δfTlowast

1L

Tlowast

1R

Tlowast

2L

Tlowast

2R

Tlowast

3L

Tlowast

3R

Tlowast

4L

Tlowast

4R

T1L

T1R

T2L

T2R

T3L

T3R

T4L

T4R

ddt

ddt

Mzxminusωzdes

vd +

v

ωz

ωzdes +

+

ax

Mzxminusβdes

Mzxdes

ωzdes

βdesMzxdes

δ micro

Xxdes

ωz β

Fzij

Xxdes

βdes

β

Fxwij

Sliding modecontrol

Sliding modecontrol



controller


controller

Tire force

Actuator torque


Sliding modecontrol

Weightedcontrol




ωzd leμg

vx


(40ms)2

(30)



βdes min β βd( 1113857(31)


vxdes vo + 1113946t

to

ax(τ)dτ (32)






mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)








(34)

where

Xydes 1113944

4


Yydes 11139444


Mydes bi 1113944

4


+ 11139444

1li Fywij + Fywij1113872 1113873

(35)



Svx vx minus vxdes

sβ βminus βdes


(36)





_sωz minusεωz

sign sωz1113872 1113873

(37)




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




2 Vehicle Model





max 11139444


may 11139444

1Fyij1113872 1113873 (2)

mbaz 11139444

1Fzsij (3)



Ix _ωx di 1113944

4








1li Fyi1 minusFyi21113872 1113873 (6)











41 31 21 11

42 32 22 12

ωZ O

Fxw41

Fyw41

α41

v41

Fxw42

Fyw42

α42v42

Fxw31

Fyw31

α31

v31

Fxw32

Fyw32

α32v32

Fxw21

δ21α21

v21

Fyw21

Fxw11

δ11α11

v11

Fyw11

Fxw22

δ22α22

v21

Fyw22

Fxw12

δ12α12

v12

Fyw12

y

x

l1l4

l2l3

bi = 2divx

vyβ

V


Fxwij

Fywij

xw

yw

vwσ

α




F1zs1 lb minus lal1

4lb minus l2ambg


4lb minus l2ambg


4lb minus l2ambg


4lb minus l2ambg

(10)

where

la l1 minus l2( 1113857 + l1 + l3( 1113857 + l1 + l4( 1113857

lb l1 minus l2( 11138572

+ l1 + l3( 11138572

+ l1 + l4( 11138572

(11)


F1zsij 1

2F1zsi

(12)


F1zwij 1

2F1zsi

+ mwijg (13)







1113888 1113889

(14)



















Fyij μDy


(20)





Pt Ff + Fw + Fi + Fj1113872 1113873vx

1000η (21)




vmax

1000η (22)





CDAjρv2i1113876 1113877

vi

1000η (23)




n vx

0377Rwio (24)


Tmax DMgR

zio (25)


0 20 40 60 80 100Slip ratio ()

0

500

1000

1500

2000

2500

3000

3500

Tire

forc

e (N

)





Te 9550Pe

ne

(26)




G(s) Tmout

Tmin

1τms + 1

(27)





3 Control Structure










Observer

PWSM controller

In-wheel motor



0

200

400

600

800

1000

1200

Torq

ue (N

m)



Longitudinal motion


controller


Upper controller


(1)(2)


Vehiclemodel


Lowercontroller

8WIDEV



_β

_ωz

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

minus2 C1 + C2 + C3 + C4( 1113857

Mvx

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Mv2xminus 1

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Iz

minus2 l21C1 + l22C2 + l23C3 + l24C41113872 1113873

Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

β

ωz

⎡⎢⎣ ⎤⎥⎦ +

2C1

Mvx

2C1l1Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

δ1 (29)



δ2v2

α2

Fy2

y

V δ1α1v1

Fy1Fy3Fy4

α4 α3

l1

l2l3

l4

x2 134


Driverinputs

2 DOF dynamic

model


Speedtracking

controller

Motorcontroller

3L

2R

2L

1R

1L

3R

4L

4R


electric vehicle

δfTlowast

1L

Tlowast

1R

Tlowast

2L

Tlowast

2R

Tlowast

3L

Tlowast

3R

Tlowast

4L

Tlowast

4R

T1L

T1R

T2L

T2R

T3L

T3R

T4L

T4R

ddt

ddt

Mzxminusωzdes

vd +

v

ωz

ωzdes +

+

ax

Mzxminusβdes

Mzxdes

ωzdes

βdesMzxdes

δ micro

Xxdes

ωz β

Fzij

Xxdes

βdes

β

Fxwij

Sliding modecontrol

Sliding modecontrol



controller


controller

Tire force

Actuator torque


Sliding modecontrol

Weightedcontrol




ωzd leμg

vx


(40ms)2

(30)



βdes min β βd( 1113857(31)


vxdes vo + 1113946t

to

ax(τ)dτ (32)






mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)








(34)

where

Xydes 1113944

4


Yydes 11139444


Mydes bi 1113944

4


+ 11139444

1li Fywij + Fywij1113872 1113873

(35)



Svx vx minus vxdes

sβ βminus βdes


(36)





_sωz minusεωz

sign sωz1113872 1113873

(37)




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



1li Fyi1 minusFyi21113872 1113873 (6)











41 31 21 11

42 32 22 12

ωZ O

Fxw41

Fyw41

α41

v41

Fxw42

Fyw42

α42v42

Fxw31

Fyw31

α31

v31

Fxw32

Fyw32

α32v32

Fxw21

δ21α21

v21

Fyw21

Fxw11

δ11α11

v11

Fyw11

Fxw22

δ22α22

v21

Fyw22

Fxw12

δ12α12

v12

Fyw12

y

x

l1l4

l2l3

bi = 2divx

vyβ

V


Fxwij

Fywij

xw

yw

vwσ

α




F1zs1 lb minus lal1

4lb minus l2ambg


4lb minus l2ambg


4lb minus l2ambg


4lb minus l2ambg

(10)

where

la l1 minus l2( 1113857 + l1 + l3( 1113857 + l1 + l4( 1113857

lb l1 minus l2( 11138572

+ l1 + l3( 11138572

+ l1 + l4( 11138572

(11)


F1zsij 1

2F1zsi

(12)


F1zwij 1

2F1zsi

+ mwijg (13)







1113888 1113889

(14)



















Fyij μDy


(20)





Pt Ff + Fw + Fi + Fj1113872 1113873vx

1000η (21)




vmax

1000η (22)





CDAjρv2i1113876 1113877

vi

1000η (23)




n vx

0377Rwio (24)


Tmax DMgR

zio (25)


0 20 40 60 80 100Slip ratio ()

0

500

1000

1500

2000

2500

3000

3500

Tire

forc

e (N

)





Te 9550Pe

ne

(26)




G(s) Tmout

Tmin

1τms + 1

(27)





3 Control Structure










Observer

PWSM controller

In-wheel motor



0

200

400

600

800

1000

1200

Torq

ue (N

m)



Longitudinal motion


controller


Upper controller


(1)(2)


Vehiclemodel


Lowercontroller

8WIDEV



_β

_ωz

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

minus2 C1 + C2 + C3 + C4( 1113857

Mvx

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Mv2xminus 1

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Iz

minus2 l21C1 + l22C2 + l23C3 + l24C41113872 1113873

Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

β

ωz

⎡⎢⎣ ⎤⎥⎦ +

2C1

Mvx

2C1l1Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

δ1 (29)



δ2v2

α2

Fy2

y

V δ1α1v1

Fy1Fy3Fy4

α4 α3

l1

l2l3

l4

x2 134


Driverinputs

2 DOF dynamic

model


Speedtracking

controller

Motorcontroller

3L

2R

2L

1R

1L

3R

4L

4R


electric vehicle

δfTlowast

1L

Tlowast

1R

Tlowast

2L

Tlowast

2R

Tlowast

3L

Tlowast

3R

Tlowast

4L

Tlowast

4R

T1L

T1R

T2L

T2R

T3L

T3R

T4L

T4R

ddt

ddt

Mzxminusωzdes

vd +

v

ωz

ωzdes +

+

ax

Mzxminusβdes

Mzxdes

ωzdes

βdesMzxdes

δ micro

Xxdes

ωz β

Fzij

Xxdes

βdes

β

Fxwij

Sliding modecontrol

Sliding modecontrol



controller


controller

Tire force

Actuator torque


Sliding modecontrol

Weightedcontrol




ωzd leμg

vx


(40ms)2

(30)



βdes min β βd( 1113857(31)


vxdes vo + 1113946t

to

ax(τ)dτ (32)






mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)








(34)

where

Xydes 1113944

4


Yydes 11139444


Mydes bi 1113944

4


+ 11139444

1li Fywij + Fywij1113872 1113873

(35)



Svx vx minus vxdes

sβ βminus βdes


(36)





_sωz minusεωz

sign sωz1113872 1113873

(37)




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



F1zs1 lb minus lal1

4lb minus l2ambg


4lb minus l2ambg


4lb minus l2ambg


4lb minus l2ambg

(10)

where

la l1 minus l2( 1113857 + l1 + l3( 1113857 + l1 + l4( 1113857

lb l1 minus l2( 11138572

+ l1 + l3( 11138572

+ l1 + l4( 11138572

(11)


F1zsij 1

2F1zsi

(12)


F1zwij 1

2F1zsi

+ mwijg (13)







1113888 1113889

(14)



















Fyij μDy


(20)





Pt Ff + Fw + Fi + Fj1113872 1113873vx

1000η (21)




vmax

1000η (22)





CDAjρv2i1113876 1113877

vi

1000η (23)




n vx

0377Rwio (24)


Tmax DMgR

zio (25)


0 20 40 60 80 100Slip ratio ()

0

500

1000

1500

2000

2500

3000

3500

Tire

forc

e (N

)





Te 9550Pe

ne

(26)




G(s) Tmout

Tmin

1τms + 1

(27)





3 Control Structure










Observer

PWSM controller

In-wheel motor



0

200

400

600

800

1000

1200

Torq

ue (N

m)



Longitudinal motion


controller


Upper controller


(1)(2)


Vehiclemodel


Lowercontroller

8WIDEV



_β

_ωz

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

minus2 C1 + C2 + C3 + C4( 1113857

Mvx

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Mv2xminus 1

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Iz

minus2 l21C1 + l22C2 + l23C3 + l24C41113872 1113873

Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

β

ωz

⎡⎢⎣ ⎤⎥⎦ +

2C1

Mvx

2C1l1Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

δ1 (29)



δ2v2

α2

Fy2

y

V δ1α1v1

Fy1Fy3Fy4

α4 α3

l1

l2l3

l4

x2 134


Driverinputs

2 DOF dynamic

model


Speedtracking

controller

Motorcontroller

3L

2R

2L

1R

1L

3R

4L

4R


electric vehicle

δfTlowast

1L

Tlowast

1R

Tlowast

2L

Tlowast

2R

Tlowast

3L

Tlowast

3R

Tlowast

4L

Tlowast

4R

T1L

T1R

T2L

T2R

T3L

T3R

T4L

T4R

ddt

ddt

Mzxminusωzdes

vd +

v

ωz

ωzdes +

+

ax

Mzxminusβdes

Mzxdes

ωzdes

βdesMzxdes

δ micro

Xxdes

ωz β

Fzij

Xxdes

βdes

β

Fxwij

Sliding modecontrol

Sliding modecontrol



controller


controller

Tire force

Actuator torque


Sliding modecontrol

Weightedcontrol




ωzd leμg

vx


(40ms)2

(30)



βdes min β βd( 1113857(31)


vxdes vo + 1113946t

to

ax(τ)dτ (32)






mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)








(34)

where

Xydes 1113944

4


Yydes 11139444


Mydes bi 1113944

4


+ 11139444

1li Fywij + Fywij1113872 1113873

(35)



Svx vx minus vxdes

sβ βminus βdes


(36)





_sωz minusεωz

sign sωz1113872 1113873

(37)




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Pt Ff + Fw + Fi + Fj1113872 1113873vx

1000η (21)




vmax

1000η (22)





CDAjρv2i1113876 1113877

vi

1000η (23)




n vx

0377Rwio (24)


Tmax DMgR

zio (25)


0 20 40 60 80 100Slip ratio ()

0

500

1000

1500

2000

2500

3000

3500

Tire

forc

e (N

)





Te 9550Pe

ne

(26)




G(s) Tmout

Tmin

1τms + 1

(27)





3 Control Structure










Observer

PWSM controller

In-wheel motor



0

200

400

600

800

1000

1200

Torq

ue (N

m)



Longitudinal motion


controller


Upper controller


(1)(2)


Vehiclemodel


Lowercontroller

8WIDEV



_β

_ωz

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

minus2 C1 + C2 + C3 + C4( 1113857

Mvx

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Mv2xminus 1

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Iz

minus2 l21C1 + l22C2 + l23C3 + l24C41113872 1113873

Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

β

ωz

⎡⎢⎣ ⎤⎥⎦ +

2C1

Mvx

2C1l1Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

δ1 (29)



δ2v2

α2

Fy2

y

V δ1α1v1

Fy1Fy3Fy4

α4 α3

l1

l2l3

l4

x2 134


Driverinputs

2 DOF dynamic

model


Speedtracking

controller

Motorcontroller

3L

2R

2L

1R

1L

3R

4L

4R


electric vehicle

δfTlowast

1L

Tlowast

1R

Tlowast

2L

Tlowast

2R

Tlowast

3L

Tlowast

3R

Tlowast

4L

Tlowast

4R

T1L

T1R

T2L

T2R

T3L

T3R

T4L

T4R

ddt

ddt

Mzxminusωzdes

vd +

v

ωz

ωzdes +

+

ax

Mzxminusβdes

Mzxdes

ωzdes

βdesMzxdes

δ micro

Xxdes

ωz β

Fzij

Xxdes

βdes

β

Fxwij

Sliding modecontrol

Sliding modecontrol



controller


controller

Tire force

Actuator torque


Sliding modecontrol

Weightedcontrol




ωzd leμg

vx


(40ms)2

(30)



βdes min β βd( 1113857(31)


vxdes vo + 1113946t

to

ax(τ)dτ (32)






mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)








(34)

where

Xydes 1113944

4


Yydes 11139444


Mydes bi 1113944

4


+ 11139444

1li Fywij + Fywij1113872 1113873

(35)



Svx vx minus vxdes

sβ βminus βdes


(36)





_sωz minusεωz

sign sωz1113872 1113873

(37)




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Te 9550Pe

ne

(26)




G(s) Tmout

Tmin

1τms + 1

(27)





3 Control Structure










Observer

PWSM controller

In-wheel motor



0

200

400

600

800

1000

1200

Torq

ue (N

m)



Longitudinal motion


controller


Upper controller


(1)(2)


Vehiclemodel


Lowercontroller

8WIDEV



_β

_ωz

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

minus2 C1 + C2 + C3 + C4( 1113857

Mvx

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Mv2xminus 1

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Iz

minus2 l21C1 + l22C2 + l23C3 + l24C41113872 1113873

Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

β

ωz

⎡⎢⎣ ⎤⎥⎦ +

2C1

Mvx

2C1l1Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

δ1 (29)



δ2v2

α2

Fy2

y

V δ1α1v1

Fy1Fy3Fy4

α4 α3

l1

l2l3

l4

x2 134


Driverinputs

2 DOF dynamic

model


Speedtracking

controller

Motorcontroller

3L

2R

2L

1R

1L

3R

4L

4R


electric vehicle

δfTlowast

1L

Tlowast

1R

Tlowast

2L

Tlowast

2R

Tlowast

3L

Tlowast

3R

Tlowast

4L

Tlowast

4R

T1L

T1R

T2L

T2R

T3L

T3R

T4L

T4R

ddt

ddt

Mzxminusωzdes

vd +

v

ωz

ωzdes +

+

ax

Mzxminusβdes

Mzxdes

ωzdes

βdesMzxdes

δ micro

Xxdes

ωz β

Fzij

Xxdes

βdes

β

Fxwij

Sliding modecontrol

Sliding modecontrol



controller


controller

Tire force

Actuator torque


Sliding modecontrol

Weightedcontrol




ωzd leμg

vx


(40ms)2

(30)



βdes min β βd( 1113857(31)


vxdes vo + 1113946t

to

ax(τ)dτ (32)






mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)








(34)

where

Xydes 1113944

4


Yydes 11139444


Mydes bi 1113944

4


+ 11139444

1li Fywij + Fywij1113872 1113873

(35)



Svx vx minus vxdes

sβ βminus βdes


(36)





_sωz minusεωz

sign sωz1113872 1113873

(37)




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Observer

PWSM controller

In-wheel motor



0

200

400

600

800

1000

1200

Torq

ue (N

m)



Longitudinal motion


controller


Upper controller


(1)(2)


Vehiclemodel


Lowercontroller

8WIDEV



_β

_ωz

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

minus2 C1 + C2 + C3 + C4( 1113857

Mvx

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Mv2xminus 1

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Iz

minus2 l21C1 + l22C2 + l23C3 + l24C41113872 1113873

Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

β

ωz

⎡⎢⎣ ⎤⎥⎦ +

2C1

Mvx

2C1l1Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

δ1 (29)



δ2v2

α2

Fy2

y

V δ1α1v1

Fy1Fy3Fy4

α4 α3

l1

l2l3

l4

x2 134


Driverinputs

2 DOF dynamic

model


Speedtracking

controller

Motorcontroller

3L

2R

2L

1R

1L

3R

4L

4R


electric vehicle

δfTlowast

1L

Tlowast

1R

Tlowast

2L

Tlowast

2R

Tlowast

3L

Tlowast

3R

Tlowast

4L

Tlowast

4R

T1L

T1R

T2L

T2R

T3L

T3R

T4L

T4R

ddt

ddt

Mzxminusωzdes

vd +

v

ωz

ωzdes +

+

ax

Mzxminusβdes

Mzxdes

ωzdes

βdesMzxdes

δ micro

Xxdes

ωz β

Fzij

Xxdes

βdes

β

Fxwij

Sliding modecontrol

Sliding modecontrol



controller


controller

Tire force

Actuator torque


Sliding modecontrol

Weightedcontrol




ωzd leμg

vx


(40ms)2

(30)



βdes min β βd( 1113857(31)


vxdes vo + 1113946t

to

ax(τ)dτ (32)






mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)








(34)

where

Xydes 1113944

4


Yydes 11139444


Mydes bi 1113944

4


+ 11139444

1li Fywij + Fywij1113872 1113873

(35)



Svx vx minus vxdes

sβ βminus βdes


(36)





_sωz minusεωz

sign sωz1113872 1113873

(37)




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


_β

_ωz

⎡⎢⎢⎢⎣ ⎤⎥⎥⎥⎦

minus2 C1 + C2 + C3 + C4( 1113857

Mvx

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Mv2xminus 1

minus2 l1C1 + l2C2 + l3C3 + l4C4( 1113857

Iz

minus2 l21C1 + l22C2 + l23C3 + l24C41113872 1113873

Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

β

ωz

⎡⎢⎣ ⎤⎥⎦ +

2C1

Mvx

2C1l1Iz

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

δ1 (29)



δ2v2

α2

Fy2

y

V δ1α1v1

Fy1Fy3Fy4

α4 α3

l1

l2l3

l4

x2 134


Driverinputs

2 DOF dynamic

model


Speedtracking

controller

Motorcontroller

3L

2R

2L

1R

1L

3R

4L

4R


electric vehicle

δfTlowast

1L

Tlowast

1R

Tlowast

2L

Tlowast

2R

Tlowast

3L

Tlowast

3R

Tlowast

4L

Tlowast

4R

T1L

T1R

T2L

T2R

T3L

T3R

T4L

T4R

ddt

ddt

Mzxminusωzdes

vd +

v

ωz

ωzdes +

+

ax

Mzxminusβdes

Mzxdes

ωzdes

βdesMzxdes

δ micro

Xxdes

ωz β

Fzij

Xxdes

βdes

β

Fxwij

Sliding modecontrol

Sliding modecontrol



controller


controller

Tire force

Actuator torque


Sliding modecontrol

Weightedcontrol




ωzd leμg

vx


(40ms)2

(30)



βdes min β βd( 1113857(31)


vxdes vo + 1113946t

to

ax(τ)dτ (32)






mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)








(34)

where

Xydes 1113944

4


Yydes 11139444


Mydes bi 1113944

4


+ 11139444

1li Fywij + Fywij1113872 1113873

(35)



Svx vx minus vxdes

sβ βminus βdes


(36)





_sωz minusεωz

sign sωz1113872 1113873

(37)




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



ωzd leμg

vx


(40ms)2

(30)



βdes min β βd( 1113857(31)


vxdes vo + 1113946t

to

ax(τ)dτ (32)






mvx_β + ωz1113872 1113873 Ydes

Iz _ωz Mzdes

(33)








(34)

where

Xydes 1113944

4


Yydes 11139444


Mydes bi 1113944

4


+ 11139444

1li Fywij + Fywij1113872 1113873

(35)



Svx vx minus vxdes

sβ βminus βdes


(36)





_sωz minusεωz

sign sωz1113872 1113873

(37)




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




ωzminusβ Ydes

mvx





1113874 1113875(39)


Vi 12s2i (40)



11138681113868111386811138681113868111386811138681113868 (41)


satsi

Δi

1113888 1113889

1si

Δi

gt 1

si

Δi

minus1lesi

Δi

lt 1

minus1si

Δi

ltminus1

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

(42)



svx

Δvx

1113888 1113889minus vyωz1113890 1113891 + f


1113874 11138751113876 1113877



sωz

Δωz


(43)











ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




ωzd gt 0

ωz

11138681113868111386811138681113868111386811138681113868lt ωzd

11138681113868111386811138681113868111386811138681113868

(45)




st Fb11 01Fb

Fb12 015Fb

Fb31 025Fb

Fb41 05Fb

(46)




Bu v (47)where


B a11 a12 a21 a22 a31 a32 a41a42

b11 b12 b21 b22 b31 b32 b41b421113890 1113891

(48)


aij cos δij


ili sin δij

(49)


minusTmmaxig

RwleFxwij le

minusTmmaxig

Rw (50)




where

uij max


ywij

1113970

Tmmaxig

Rw

1113888 1113889

uij min


ywij

1113970

Tmmaxig

Rw

1113888 1113889

(52)





21

11

31

41

22 13

242

11

Actual

Desired

50 25

15 10

nablaMzb




J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



J2 Wuu2 (55)





(56)


















Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







Start

Yes

No

Yes

No

End


k gt i + j


pk = 0





Wk+1 = Wk cup ik

Wk+1 = Wk

xOptimumsolution

Yes

No

Yes

Calculateαk xk+1






0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





0 2 4 6 8 10Time (s)

0

20

40

60

Stee

ring

angl

e δ (d

eg)


(a)

0 2 4 6 8 10Time (s)

0

2

4

6

Yaw

rate

ωz (

deg

s)


(b)

0 2 4 6 8 10Time (s)

0

05

1

15

2

25

Late

ral a

ccel

erat

ion a y

(ms

2 )


(c)

0 2 4 6 8 10Time (s)

0

05

1Ro

ll an

gle ϕ

(deg

)


(d)




0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


0 100 200 300X (m)

ndash6

ndash4

ndash2

0

2

4

Y (m

)


(a)


0 5 10 15 20 25Time (s)

0

10

20

30

40

50

Long

itudi

nal s

peed

v x (k

mh

)

(b)


0 5 10 15 20 25Time (s)

ndash200

ndash100

0

100

200

300

Stee

ring

angl

e δ (d

eg)

(c)


0 5 10 15 20 25Time (s)

ndash30

ndash20

ndash10

0

10

20

Yaw

rate

ωz (

deg

s)

(d)


0 5 10 15 20 25Time (s)

ndash2

0

2

4

Roll

angl

e ϕ (d

eg)

(e)


0 5 10 15 20 25Time (s)

ndash5

ndash3

ndash1

1

3

56

Late

ral a

ccel

aret

ion a y

(ms

2 )

(f )









Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Vehicle model

ESC model

Simulink

AutoBox

Driversignals


TCPIP

PC

HIL

VCU


ACDC


VCU

Pedel

dSPACEAutoBox

CAN bus






0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





0 100 200 300 400X (m)

0

2

4Y

(m)

DesiredDYCESC

(a)

0 5 10 15Time (s)

997

998

999

100

Long

itudi

nal s

peed

(km

h)

DYCESC

(b)

DYCESC

0 5 10 15Time (s)

ndash005

0

005

Yaw

rate

ωz (

rad

s)

(c)

DYCESC

0 5 10 15Time (s)

ndash5

0

5

Side

slip

angl

e β (r

ads

) times10ndash3

(d)

DYCESC

Side

slip

angl

e β (r

ads

) times10ndash3

0 5 10 15Time (s)

ndash5

0

5

(e)

DYCESC


ndash001

0

001

Side

slip

angl

e rat

e dβ

(rad

s)

times10ndash3

(f )







Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Data Availability


0 5 10 15Time (s)

ndash200

ndash100

0

100

200

Torq

ue (N

middotm

)

1l1r

2l2r

(a)

0 5 10 15Time (s)

ndash100

ndash50

0

50

100

150

Torq

ue (N

middotm

)

3l3r

4l4r

(b)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

1l1r

2l2r

(c)

0 5 10 15Time (s)

ndash400

ndash200

0

200

Torq

ue (N

middotm

)

3l3r

4l4r

(d)





Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Electronic Stability Control for Improving Stability for...

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Transcript of Electronic Stability Control for Improving Stability for...